Create a 2D grid to map points over a transformation?

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Shovnik Paul 2022-2-10

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https://ww2.mathworks.cn/matlabcentral/answers/1647315-create-a-2d-grid-to-map-points-over-a-transformation

编辑： Shovnik Paul 2022-2-10

conformal_mapping.png

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I am trying to create two plots: one showing a grid on the top and the second showing a transformation applied to every point on the grid (bottom). Till now I have been able to figure out the following way which only works when the x and y ranges are symmetric:

x = linspace(-5, 5, 10);

y = linspace(-5, 5, 100);

[X, Y]= meshgrid(x, y);

figure

plot(X, Y, 'blue', Y, X, 'blue');

Z = X + i*Y;

W = Z.^2; % f(z) = z^2 for example

figure

plot(W, 'blue')

Z = Y + i*X;

W = Z.^2;

hold on;

plot(W, 'blue')

So far so good but say I want to create grid that is asymetrical with regards to the axes ranges. For example, the normalized impedance of a transmission line z = r + ix which can only have positive resistance r. Say want a grid in the region 0 < r < 10 and -10 < x < 10 with lines at intervals of 1 say. Is there a general way of doing this? (and perhas a better way of doing the above?)